Turn sample strata into population-corrected estimates fast now. See weights, variance, and confidence intervals instantly. Export tables to share with teams and stakeholders securely.
| Stratum | Population Nh | Sample nh | ȳh (estimate) | sh (SD) |
|---|---|---|---|---|
| Urban | 5,200 | 180 | 0.62 | 0.48 |
| Rural | 3,800 | 120 | 0.54 | 0.50 |
| Peri-urban | 1,000 | 50 | 0.58 | 0.49 |
Post-stratification adjusts a sample estimate using known population stratum sizes. Let strata be indexed by h = 1..H, with population size Nh, total population N = Σ Nh, and a stratum-level sample estimate ȳh.
If a within-stratum sample standard deviation sh is provided, an approximate variance is:
Post-stratification corrects sample imbalance by aligning estimates with known population totals. Typical strata include age bands, sex, region, education, or urbanicity. The tool uses population counts Nh to compute weights Wh=Nh/N, so every stratum contributes in proportion to its true share, not its sample share. When your sample over-represents a stratum, post-stratification automatically down-weights it and lifts under-represented groups.
Large weights often signal under-sampled groups. Review Wh and the contribution Wh·ȳh for each stratum. If one stratum supplies most of the estimate, consider improving sampling or combining sparse categories. As a rule, very small nh with large Nh can increase variance and widen intervals. Track the maximum weight and the ratio of largest to smallest weights to spot instability.
When you provide within-stratum SD sh, the calculator approximates Var(ŶPS)≈Σ(Wh2·sh2/nh)·(1−fh). The finite population correction fh=nh/Nh reduces variance when sampling fractions are meaningful, especially in small frames. For proportions, sh can be estimated as √(ph(1−ph)) if microdata SD is unavailable.
Ensure all Nh are positive and that nh≤Nh. For proportions, keep ȳh between 0 and 1; for means, use consistent units across strata. Missing sh prevents standard errors, so add SD from your microdata or a prior study to produce comparable confidence bounds. If a stratum has nh=1, its SD-based variance is fragile; merge it with a similar group where possible.
The results panel summarizes the post-stratified estimate, total population N, and stratum contributions. Export the CSV to audit weights and document assumptions; export the PDF for quick sharing. Include strata definitions, source of Nh, confidence level, and whether FPC was applied, so readers can reproduce the adjustment and interpret its limits. Also report the unadjusted sample estimate alongside the adjusted estimate to show the impact of calibration in practical survey workflows.
Provide at least one stratum with population size Nh, sample size nh, and a stratum estimate ybar. Add SD per stratum if you want standard error and confidence intervals.
Use mean for continuous measures like income, score, or time. Use proportion for binary or rate outcomes scaled from 0 to 1, such as adoption, prevalence, or success probability.
Enable FPC when nh is a noticeable share of Nh, such as in small lists or census-like samples. FPC lowers variance by multiplying by (1−nh/Nh), giving tighter intervals.
Compute SD from the raw stratum observations when available. For a proportion, a common approximation is sqrt(p*(1−p)). If you only have historical studies, reuse the closest SD and document it.
Contribution equals Wh multiplied by ybarh, so large strata or extreme ybarh values drive the total. If dominance comes from tiny nh, consider better sampling, collapsing categories, or sensitivity checks.
They are unbiased only if strata totals are correct and within each stratum the sample is representative of that stratum. If nonresponse or measurement error differs by stratum, adjustment may still be biased.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.